The plan, proposed by investors including the Church of England, was supported by over 62% of those eligible to vote.
The vote comes amid US media reports that President Trump is poised today to pull out of the Paris climate agreement.
Exxon will now have to consider how global efforts to mitigate climate change will impact their business.
Previous attempts by activists to force the company to take the impact of climate change into account had failed, with the motion gaining support from just over 38% of shareholders last year.
The resolution, filed by the Church Commissioners for England and New York State Comptroller Thomas P DiNapoli, asked Exxon to report on how its business model will be affected by global efforts to limit the average rise in temperatures to below 2C.
While the motion is non-binding, commentators think there will be increased pressure on the company to report on the impacts of climate change and the restrictions on fossil fuels being considered as part of the Paris climate agreement.
Exxon Mobil was one of the last hold-outs among major oil companies on the issue of climate change, with other major producers including BP PLC (LON:BP.) and ConocoPhillips Inc (NYSE:COP) already publishing reports on how rising temperatures would impact their businesses.